Inverse Problems

Methods of Solving Ill-Posed Problems.- One-Dimensional Inverse Scattering and Spectral Problems.- Inverse Obstacle Scattering.- Stability of the Solutions to 3D Inverse Scattering Problems with Fixed-Energy Data.- Non-Uniqueness and Uniqueness Results.- Inverse Problems of Potential Theory and Other Inverse Source Problems.- Non-Overdetermined Inverse Problems.- Low-Frequency Inversion.- Wave Scattering by Small Bodies of Arbitrary Shapes.- The Pompeiu Problem.

From the reviews of the first edition:"The author’s attention is addressed … to inverse problems for scattering theory … . the reviewer emphasizes the author’s effort of simplifying both the results in the mathematical literature and his own ones as well as the effort of unifying the theory of the inverse problems illustrated. Moreover, the proofs of the various propositions are almost always inserted in the book so that we can say the volume is friendly to readers … . Finally, the proofs are well written … ." (Alfredo Lorenzi, Zentralblatt MATH, Vol. 1083, 2006)“This book is devoted to the investigation of inverse problems for PDEs, in particular, to the theory of inverse spectral problems and inverse scattering problems. … Graduate students and researchers will find in this work extensive reference material including a collection of relevant classical results as well as several new developments in the area of inverse and ill-posed problems.” (Antonio C. G. Leitão, Mathematical Reviews, Issue 2012 k)